16r^2-8r-1=0

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Solution for 16r^2-8r-1=0 equation:


Simplifying
16r2 + -8r + -1 = 0

Reorder the terms:
-1 + -8r + 16r2 = 0

Solving
-1 + -8r + 16r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
-0.0625 + -0.5r + r2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + -0.5r + 0.0625 + r2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + -0.5r + r2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + -0.5r + r2 = 0 + 0.0625
-0.5r + r2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
-0.5r + r2 = 0.0625

The r term is -0.5r.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5r + 0.0625 + r2 = 0.0625 + 0.0625

Reorder the terms:
0.0625 + -0.5r + r2 = 0.0625 + 0.0625

Combine like terms: 0.0625 + 0.0625 = 0.125
0.0625 + -0.5r + r2 = 0.125

Factor a perfect square on the left side:
(r + -0.25)(r + -0.25) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(r + -0.25) equal to 0.353553391 and -0.353553391.

Subproblem 1

r + -0.25 = 0.353553391 Simplifying r + -0.25 = 0.353553391 Reorder the terms: -0.25 + r = 0.353553391 Solving -0.25 + r = 0.353553391 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + r = 0.353553391 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + r = 0.353553391 + 0.25 r = 0.353553391 + 0.25 Combine like terms: 0.353553391 + 0.25 = 0.603553391 r = 0.603553391 Simplifying r = 0.603553391

Subproblem 2

r + -0.25 = -0.353553391 Simplifying r + -0.25 = -0.353553391 Reorder the terms: -0.25 + r = -0.353553391 Solving -0.25 + r = -0.353553391 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + r = -0.353553391 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + r = -0.353553391 + 0.25 r = -0.353553391 + 0.25 Combine like terms: -0.353553391 + 0.25 = -0.103553391 r = -0.103553391 Simplifying r = -0.103553391

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.603553391, -0.103553391}

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